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Semiconductor Physics and Devices: Basic Principles, 4
th
 edition Chapter 6 
By D. A. Neamen Problem Solutions 
______________________________________________________________________________________ 
 
6.9 
 p-type material; 
 minority carriers are electrons 
(a) n  
 From Figure 5.3, 1300n cm 2 /V-s 
(b)   13000259.0





 nn
e
kT
DD  
 67.33 cm 2 /s 
(c) 7
0 10 nnt  s 
 15107 ao Np cm 3 
 
 
15
2102
107
105.1



a
i
o
N
n
n 
 
41021.3  cm 3 
 
pt
o
nt
o pn

 
 
pt
15
7
4 107
10
10214.3 



 
 so 
41018.2 pt s 
_______________________________________ 
 
6.10 
 For Ge: 13104.2 in cm 3 
 2
2
22
i
dd
o n
NN
n 





 
  213
2
1313
104.2
2
104
2
104







 


 
 
1310124.5  cm 3 
 
  13
13
2132
10124.1
10124.5
104.2




o
i
o
n
n
p cm 3 
(a) We have: 
 3900n cm 2 /V-s, 101nD cm 2 /s 
 1900p cm 2 /V-s, 2.49pD cm 2 /s 
 For very, very low injection, 
 
 
pDnD
pnDD
D
pn
pn


 
 
   
     1313
1313
10124.12.4910124.5101
10124.110124.52.49101


 
 2.54 cm 2 /s 
 and 
 
 
 
 
 
 
pn
np
pn
pn





 
   
     1313
1313
10124.1190010124.53900
10124.510124.119003900


 
 1340 cm 2 /V-s 
(b) For holes, 
6
0 102  ppt  s 
For electrons, 
 
0pnt
pn

 
 
6
1313
102
10124.110124.5




nt
 
61012.9  nt s 
_______________________________________ 
 
6.11 
 pene pn   
 With excess carriers 
 nnn o  and ppp o  
 For an n-type semiconductor, we can write 
 ppn   
 Then 
    ppepne opon   
 or 
   pepene pnopon   
 so 
   pe pn   
 In steady-state, pOgp   
 So that 
   pOpn ge   
_______________________________________ 
 
6.12 
(a) 1610 ao Np cm 3 
 
  4
16
2102
1025.2
10
105.1



o
i
o
p
n
n cm 3 
    ppenne opon   
   nepe pnop   
 Now  0/
0 1 nt
n egpn
 
 
    0/720 1105108 nt
e
  
  0/14 1104 nt
e

 cm 3